Math Problem Statement
Graph the linear equation 5x + 5y = 15.
Solution
The equation to graph is:
Steps to Graph the Equation:
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Simplify the equation: Divide the entire equation by 5 to simplify: Now, we have the equation in a simpler form.
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Rewrite in slope-intercept form: This equation is in the form , where:
- is the slope (indicating a downward slope),
- is the y-intercept (the point where the line crosses the y-axis).
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Plot the y-intercept:
- Start by plotting the point (0, 3) on the y-axis.
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Use the slope:
- The slope is -1, which means for every 1 unit you move to the right along the x-axis, move 1 unit down.
- From the point (0, 3), move right 1 unit and down 1 unit to get the point (1, 2). Plot this point.
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Draw the line:
- Draw a straight line through the points (0, 3) and (1, 2), extending in both directions.
Would you like me to generate a graph for this equation?
Follow-up Questions:
- What is the importance of slope-intercept form in graphing linear equations?
- How do you find the slope from a linear equation in standard form?
- What does the y-intercept tell you about the graph of a linear equation?
- Can you convert any linear equation into slope-intercept form?
- How can you check if a point lies on the graph of a linear equation?
Tip:
When graphing a linear equation, always start by identifying the y-intercept and the slope, as they provide a clear starting point and direction for the line.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Slope-Intercept Form
Formulas
Standard form of a linear equation: Ax + By = C
Slope-Intercept form: y = mx + b
Theorems
Linear graphing using slope and intercept
Suitable Grade Level
Grades 8-10